The Kelly Criterion is a formula that calculates the exact percentage of your account to risk on each trade. Give it your historical win rate and your average win-to-loss ratio, and it returns the position size that grows your account at the fastest possible rate over a long series of trades.
The formula is mathematically correct. The problem is using it in trading, where both inputs are difficult to measure and the output can recommend sizes that will damage your account before your edge has time to prove itself.
Key Takeaways
- The Kelly Criterion is a position sizing formula developed by John L. Kelly Jr. in 1956 that calculates the optimal fraction of capital to risk per trade.
- The formula requires your win rate and average win-to-loss ratio, and both need a large sample of trades before they're reliable.
- Full Kelly maximizes long-run growth but generates drawdowns most traders won't hold through.
- Most traders use fractional Kelly, typically 25 to 50% of the full output, to cut variance without gutting long-run growth.
- Kelly is most useful as a ceiling on position size and as a tool for comparing the strength of different strategies.
Table of Contents
- What the Kelly Criterion Is
- The Kelly Formula
- Why Full Kelly Is Dangerous in Practice
- Fractional Kelly
- Getting Your Inputs Right
- Kelly vs Other Position Sizing Methods
- When to Use the Kelly Criterion
What the Kelly Criterion Is
John L. Kelly Jr. developed the formula at Bell Labs in 1956. His original paper, "A New Interpretation of Information Rate," focused on signal transmission and information theory, not markets. The connection to trading came later.
Ed Thorp, a mathematician who later ran the hedge fund Princeton Newport Partners, applied Kelly's framework to blackjack in his 1962 book "Beat the Dealer" and then to financial markets in subsequent decades. Princeton Newport ran for over 20 years without a losing year, and Thorp's position sizing approach drew directly from Kelly's framework.
Kelly's core insight is that there is a precise fraction of capital to allocate at any given edge. Allocate too little and your account grows slower than it could. Allocate too much and a losing streak destroys capital faster than your edge can recover it. The formula locates the optimal point between those two outcomes.
The Kelly Formula
The version traders use is:
f* = W - (1 - W) / R
Where:
- f* is the fraction of your account to risk per trade
- W is your win rate expressed as a decimal (0.55 for 55%)
- R is your average winning trade divided by your average losing trade
Some sources use odds notation from the original Bell Labs paper. The version above produces the same result and maps directly onto a trading log.
If f* comes out negative, your strategy has a negative expected value. The formula is telling you not to trade that system.
A Kelly Criterion Example
Take these numbers from a trading log: 55% win rate, average winner of $300, average loser of $200.
R = 300 / 200 = 1.5
f* = 0.55 - (0.45 / 1.5) = 0.55 - 0.30 = 0.25
Kelly says to risk 25% of your account on each trade. On a $10,000 account, that's $2,500 per trade.
Use the Kelly Criterion Calculator to run your own numbers. It calculates full Kelly, half-Kelly, and quarter-Kelly outputs from your win rate and reward-to-risk ratio in seconds.
Why Full Kelly Is Dangerous in Practice
Kelly maximizes the geometric growth rate of your account. That is a statement about what happens across thousands of trades, not what happens over the next two months.
Thorp's research on Kelly sizing in financial markets found that full Kelly produces drawdowns of 50% or more, even for strategies with a genuine edge. A 50% drawdown requires a 100% return just to break even. On a $10,000 account, you'd need to climb from $5,000 back to $10,000 before you're back to flat.
The formula also assumes you hold your position size constant through the entire drawdown and let the edge play out. Most traders won't. A 40% drawdown at trade 47 of what turns out to be a 50-trade losing streak will break discipline before the math has a chance to work. Full Kelly delivers on its growth promise only to a trader who never adjusts sizing and never stops trading.
Fractional Kelly
Fractional Kelly means applying a percentage of the formula's output instead of the full recommended size. Half-Kelly is the most common choice, meaning you risk 50% of what the formula produces.
Using the example above, half-Kelly brings the risk per trade from 25% down to 12.5%. Quarter-Kelly brings it to 6.25%.
Van Tharp's work on position sizing shows that half-Kelly cuts variance by roughly 75% while reducing long-run growth rate by about 25%. That's a worthwhile exchange for any trader who has to survive the drawdowns in real time rather than observe them on a backtest.
| Kelly Fraction | Risk Per Trade (example) | Variance vs Full Kelly | Growth Rate vs Full Kelly |
|---|---|---|---|
| Full Kelly | 25% | Baseline | 100% |
| Half-Kelly | 12.5% | ~75% lower | ~75% |
| Quarter-Kelly | 6.25% | ~94% lower | ~50% |
The right fraction depends on confidence in your inputs. If you have 500 trades of data and your edge has held across different market conditions, half-Kelly is defensible. If you have 40 trades from a single trending market, quarter-Kelly or lower reflects what you can verify.
Getting Your Inputs Right
Kelly needs two numbers: win rate and average win-to-loss ratio. Both are easy to calculate from a trading log. Both are unreliable when measured from a small sample.
Win rate is the one that misleads traders most. After 30 trades, your observed win rate can sit 15 to 20 percentage points above or below your true rate from random variance alone. A trader with a genuine 55% win rate might observe 38% or 72% over 30 trades. Running Kelly on either number produces a position size that doesn't reflect your real edge.
Average win-to-loss ratio has its own problems. One outlier trade, a large winner that doesn't represent how you normally execute, can pull the average up. Strip outliers that don't reflect standard execution before calculating R.
The minimum sample size to trust Kelly inputs is debated, but fewer than 200 trades isn't enough for meaningful confidence. A trading journal is the only way to build that sample, and the journal earns its place for other reasons long before you have enough data to run Kelly with confidence.
Kelly vs Other Position Sizing Methods
Most traders size positions with fixed fractional risk: a fixed percentage, typically 1 to 2%, per trade regardless of measured edge. Kelly differs in one key way: it scales with your edge. A higher win rate and better R produces a higher Kelly output. A weaker edge produces a lower one. Fixed fractional treats every strategy identically.
The contrast with the Martingale strategy is more direct. Martingale increases position size after a loss, which Kelly never suggests. Kelly is structurally anti-Martingale: it scales with measured edge, not with recent trade outcomes. A losing streak doesn't change your Kelly output unless you update your win rate estimate.
Fixed dollar sizing, risking the same dollar amount per trade regardless of account size, is simpler but doesn't preserve the fractional relationship as your account grows or shrinks. Kelly and fixed fractional both scale automatically.
| Method | Scales with account size | Adjusts for edge | Drawdown risk |
|---|---|---|---|
| Fixed dollar | No | No | Low to moderate |
| Fixed fractional | Yes | No | Moderate |
| Full Kelly | Yes | Yes | High |
| Fractional Kelly | Yes | Yes | Moderate |
When to Use the Kelly Criterion
Kelly's clearest use is as a ceiling. If Kelly says 25% and you're risking 2% per trade, you're trading well within the formula's bounds. If Kelly says 3% and you're risking 5%, the formula is telling you that position size isn't supported by your edge.
You can also use Kelly to compare strategies. Two systems with different win rates and R values produce different Kelly outputs. The higher output indicates a stronger edge, even if you don't trade either system at the Kelly-recommended size. That comparison is useful when deciding which setup deserves more focus and more screen time.
Another practical application is filtering new systems before going live. Run Kelly on your paper trading or backtest data. If the output is below 2 to 3%, execution costs and real-world slippage will likely erase the edge before it has a chance to compound. That's worth knowing before you put capital at risk.
Your risk-to-reward ratio on each trade feeds directly into Kelly's R input. Track both in your journal and you have the numbers Kelly needs from your own data, not from estimates you made on a spreadsheet before you'd taken a single trade.
